Method and device for creating curved surfaces

ABSTRACT

A memory is provided with an input of such data as section data and section curve data provided on a blueprint, and a cylindrical intermediate section generating device generates an intermediate section based on the data in accordance with a cylindrical intermediate section generating method selected from a plurality of such methods. A cylindrical intermediate section curve generating device generates an intermediate section curve based on the data in accordance with a cylindrical intermediate section curve generating method selected from a plurality of such methods. A tape creation control unit effects a conversion into a machine tool NC tape format based on the intermediate section and section curves.

DESCRIPTION

1. Technical Field

This invention relates to a method of creating the curved surface of athree-dimensional body and, more particularly, to a method of creatingcurved surfaces that is ideal for the preparation of a numerical controltape required for the numerically controlled machining of athree-dimensional metal mold or the like.

2. Background Art

A curved surface of a three-dimensional metal mold or the like, whendrawn out on the plane of a blueprint, is generally represented by aplurality of given section curves, but no data is shown for the shape ofthe area lying between a certain section curve and the next adjacentsection curve. When carrying out numerically controlled machining it isessential that these two section curves be connected smoothly despitethe fact that the shape of the area between them is not given. In otherwords, this means that machining must be performed by generating thecurved surface between the two section curves from such data as thatindicative of the section curves, punching an NC tape so as toincorporate the data concerning the generated curved surface, and thenmachining the workpiece in accordance with the instructions on the NCtape. To this end, the numerical control tape ordinarily is prepared byusing a computer, and either of two methods can be adopted to create thecurved surface, namely (1) a patch system in which processing isexecuted by partitioning a curved surface into minute portions, and (2)a system in which a two-dimensional curve made of straight line segmentsand arcs is modified for each pick-feed applied to a third axis.

The patch system (1), however, entails the processing of largequantities of data as well as highly complicated mathematicalprocessing, and requires a large-scale computer system. The system (2)makes processing with a small-scale computer possible, but there is nothree-dimensional tool offset capability and an excessive limitationupon tool movement direction and machining shape, making it impossibleto create sophisticated three-dimensional bodies.

Accordingly, the inventors have already proposed a method of creatingcurved surfaces, comprising generating a plurality a planar intermediatesections and finding a section curve in each intermediate section, inaccordance with predetermined rules, from section data specifying givensections (sections lying on planes) of a three-dimensional body and fromdata specifying section curves in said sections, and generating thecurved surface of the three dimensional body based on each of thesection curves in the plurality of generated intermediate sections. Inaccordance with such method, processing can be carried out with asmall-scale computer and a sophisticated three-dimensional body can becreated in a simple manner.

Nevertheless, according to the aforementioned previously proposed methodof creating curved surfaces, a disadvantage is that the curved surfaceof a three-dimensional body cannot be created in a case where the givendata is section data specifying cylindrical sections and section curvedata for curves in the cylindrical sections. More specifically, formachining a three-dimensional metal mold or the like, it is required tomachine, say, a curved surface SS1 bounded by curves CV1 through CV4, asshown in FIG. 1. The curved surface SS1 is bounded, however, by thecurves CV1, CV2 (namely cylindrical section curves) lying on thesurfaces of respective first and second cylinders CYL1, CYL2, by planesPL1, PL2, and by the curves CV3, CV4 (namely planar section curves) inthe respective planes PL1, PL2. In consequence, the curved surface SS1cannot be created with the method of creating curved surfaces previouslyproposed.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a novel method ofcreating curved surfaces in which, in a case where cylindrical sectionsand the section curves lying in the cylindrical sections are given, thecurved surface bounded by these section curves can be created in asimple manner, and in which processing is capable of being executed by asmall-scale computer. The present invention creates a curved surfacefrom a plurality of section curves that are classified broadly intogiven cylindrical section curves and reference curves. In creating thecurved surface, the given cylindrical section curves are those whichserve as the basis for generating cylindrical intermediate sectioncurves. The reference curves are those which are utilized in determiningthe positions of the cylindrical intermediate sections and in decidingthe shapes of the cylindrical intermediate section curves. In generatingthe curved surface, the inputs to the processor of a computer aresection data relating to sections and reference surfaces, and sectioncurve data relating to section curves and reference curves, these itemsof data appearing on a blueprint. Upon being supplied with these itemsof data, the processor executes processing for creating the curvedsurface, namely processing for generating cylindrical intermediatesections, cylindrical intermediate section curves, and the curvedsurface proper.

According to the present invention, two methods of generatingcylindrical intermediate sections are disclosed, as well as four methodsof executing the processing for generating the cylindrical intermediatesection curves in accordance with which sections have their sectioncurve data given on the blueprint to specify the cylindricalintermediate section curves. Processing for generating these cylindricalintermediate sections and cylindrical intermediate section curves isthen repeated a number of times to connect the given section curveswhich have been obtained, thereby creating a smooth curved surface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustrative view of a curved surface bounded bycylindrical section curves and the like;

FIGS. 2(a) and 2(b) are an illustrative views for describing, insimplified form, the creation of a surface according to the presentinvention;

FIGS. 3, 4(a) and 4(b) are illustrative views for describing methods ofgenerating intermediate sections according to the present invention;

FIGS. 5(a) to 5(d) are illustrative view for describing a method ofgenerating a cylindrical intermediate section curve according to thepresent invention;

FIGS. 6(a) and (b) are an illustrative views for describing a method ofentering data;

FIGS. 7(a) to 7(f) are illustrative views for describing a method I ofgenerating a cylindrical intermediate section curve;

FIGS. 8(a) to 8(d) are illustrative views for describing a method II ofgenerating a cylindrical intermediate section curve;

FIGS. 9(a) to 9(d) are illustrative views for describing a method III ofgenerating a cylindrical intermediate section curve;

FIGS. 10(a) and 10(b) are illustrative views for describing a method IVof generating a cylindrical intermediate section curve;

FIGS. 11(a) to 11(e) illustrate curved surfaces created by the presentinvention; and

FIG. 12 is a block diagram of a curved surface generating apparatus forpracticing the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

For a fuller understanding of the present invention, reference will nowbe had to the accompanying drawings to describe an embodiment of theinvention in detail.

FIG. 2(a) is a schematic illustrative view for describing a method ofcreating a surface according to the present invention. In accordancewith the invention, a curved surface is created through the followingsteps. It will be assumed that two cylindrical sections and sectioncurves lying in these cylindrical sections are given. The steps are:

(1) generating a plurality of cylindrical intermediate sections 104, 105. . . between cylindrical sections 101, 102 that are given (referred toas given cylindrical sections);

(2) generating cylindrical intermediate section curves 104a, 105a, lyingin respective ones of the cylindrical intermediate sections generated instep (1), from given cylindrical section curves 101a, 102a that lie inthe given cylindrical sections 101, 102; and

(3) generating the curved surface [FIG. 2(b)] in the form of acontinuous series of cylindrical intermediate section curves uponfinding these cylindrical intermediate section curves 104a, 105a . . .in a number of the cylindrical intermediate sections.

The method of creating curved surfaces according to the presentinvention is therefore based upon generating both cylindricalintermediate sections and cylindrical intermediate section curves on thesurfaces of these cylindrical intermediate sections, in a manner asdescribed above.

As shown in FIGS. 3, 4(a) and 4(b), there are two methods of generatingcylindrical intermediate sections in accordance with the given sectionsand section curves drawn out on a blueprint.

(1) When one cylindrical section is given:

In a case where one cylindrical section 101 is given, cylindricalintermediate sections 104, 105, 106 . . . are generated concentricallywith respect to the given cylindrical section 101 (FIG. 3) [Method I ofgenerating cylindrical intermediate sections].

(2) When two or more cylindrical sections are given:

In a case where two cylindrical sections 101, 102 of radii R1, R2 aregiven having their central axes O1, O2 lying in parallel, with one ofthe given cylindrical sections 101 being contained in the other givencylindrical section 102, cylindrical intermediate sections 104, 105 aregenerated in such a manner that the central axis O is shiftedsuccessively from central axis O1 to central axis O2, that the radius Rgrows successively larger from R1 to R2, and that the generatedcylindrical intermediate sections do not intersect the cylindricalsections 101, 102 FIGS. 4(a) and 4(b) [Method II of generatingcylindrical intermediate sections].

As shown in FIGS. 5(a) to 5(d), there are four methods of generatingcylindrical intermediate section curves in accordance with the sectioncurves similarly drawn out on the plane of the blueprint. The methodsare as follows:

(1) generating a cylindrical intermediate section curve 103a in thecylindrical intermediate section 103 from the two given cylindricalsection curves 101a, 102a and a reference curve 111a given on one planarreference surface 111 [FIG. 5(a)] [Method I of generating cylindricalintermediate section curves];

(2) generating the cylindrical intermediate section curve 103a in thecylindrical intermediate section 103 from one given cylindrical sectioncurve 101a and reference curves 111a, 112a given in two planar referencesurfaces 111, 112 [FIG. 5(b)] [Method II of generating cylindricalintermediate section curves];

(3) generating the cylindrical intermediate section curve 103a in thecylindrical intermediate section 103 from the two given cylindricalsection curves 101a, 102a and the reference curves 111a, 112a given inthe two planar reference surfaces 111, 112 [FIG. 5(c)] [Method III ofgenerating cylindrical intermediate section curves]; and

(4) generating the cylindrical intermediate section curve 103a in thecylindrical intermediate section 103 from the two given cylindricalsection curves 101a, 102a [FIG. 5(d)] [Method IV of generatingcylindrical intermediate section curves].

The foregoing is a general description of the inventive method ofcreated curved surfaces. With this as a background, the presentinvention will now be described in greater detail.

The present invention generates surfaces from a plurality of sectioncurves, these being classified into "given cylindrical section curves"and "reference curves" depending upon differences in their manner ofuse. Specifically, a "given cylindrical section curve" is a sectioncurve obtained when a curved body is cut by a given cylindrical section,while a "reference curve" is a section curve obtained when a curved bodyis cut by a given planar surface. In the creation of a curved surface, agiven cylindrical section curve is a curve upon which the generation ofa "cylindrical intermediate section curve" is based. The reference curveis a curve utilized to decide the position of a cylindrical intermediatesection and to determine the shape of a cylindrical intermediate sectioncurve. Hereafter, a plane which contains a reference curve is referredto as a "reference surface", a surface which contains the givencylindrical section curve is referred to as a "given cylindricalsurface", and a surface which contains a cylindrical intermediatesection curve is referred to as an "intermediate cylindrical surface".

When creating a curved surface, a processor, which will be describedlater, must be supplied with input data, specifically section datarelating to the sections and reference surfaces represented on the planeof a blueprint, and section curve data relating to the section curvesand reference curves which are also drawn out on the blueprint. A datainput method in accordance with the present invention will now bedescribed assuming that the curved surface to be created is the curvedsurface SS1 shown in FIG. 6(a).

[I] Data input processing {1} Inputting of curves CV1, CV2, CV3 and CV4

(1) One side surface of cylindrical surface 101 is cut and developed,and the given cylindrical section curve CV1 is transformed to place itin an H-θ plane. It should be noted that the θ-axis indicates the angleof rotation from 0 to 360 degrees when the cut side surface is at 0degrees, and that the H-axis indicates the height from the origin. Herewe shall assume that the given cylindrical section curve CV1 is composedof a series of three connected arcs C1, C2, C3, as shown in FIG. 6(b),and that the starting and end points of each arc C1, C2, C3 are (P0,P1), (P1, P2), (P2, P3), respectively. Further, if we adopt CV1 as theterm for the given cylindrical section curve on the cylindrical surface101, then the section curve CV1 is defined in the following manner andthen fed into the processor:

CV1=*

P0 (. . . . )

C1 (. . . . ), P1 (. . . . )

C2 (. . . . ), P2 (. . . . )

C3 (. . . .), P3 (. . . . )

The center and radius of the arc Ci are specified within the parenthesesfollowing Ci, and the coordinates of the point Pi are specified withinthe parentheses following Pi.

(2) Next, the terms CV2, CV3, CV4 are similarly assigned to the sectioncurves in the given cylindrical section 102 and reference surface 112,and these section curves are defined in the manner described above andthen fed into the processor.

It should be noted that while three connected arcs were taken asconstructing the given cylindrical section curve CV1, a section curveCVi generally is not limited to arcs alone but is defined as a curvecomposed of line segments and a given series of points which aresmoothly connected.

After the section curves CVi (i=1,2,3,4) in the respective sections havebeen defined by observing the aforementioned steps (1) and (2) and thenapplied to the processor as inputs, the curved surface SS1 is defined asshown below using the aforesaid section curves, and is then fed into theprocessor.

{2} Entry of surface SS1

The entry of the curved surface SS1 is performed after the curvedsurface has been defined in the following manner:

    SS1=1222, BC1 (CV3, . . . ),, BC2 (CV4, . . . ),, DC1 (CV1, . . . ),, DC2 (CV2, . . . ).

Here the number 1222 is a type number that represents the type of curvedsurface that is to be generated; it allows curved surfaces of varioustypes to be specified in accordance with the particular objective. BC1(CV1, . . . ) represents a reference curve. The curve CV1 is alreadydefined. The same is true for BC2 (CV2, . . . ). DC1 (CV3, . . . ) andDC2 (CV4, . . . ) are indicative of given cylindrical section curves. Itshould be noted that data specifying the cylindrical shape, such as thedirection of the central axis, the radius and the position of theorigin, is defined within the parentheses following DCi.

The processor, once provided with the input data, begins processing tocreate the curved surface. This is done by performing the processing forcylindrical intermediate section generation, for cylindricalintermediate section curve generation and, finally, for generation orcreation of the curved surface.

[II] Processing for cylindrical intermediate section generation

A cylindrical intermediate section is generated through use of theMethods I or II of generating cylindrical intermediate sections,described above, in accordance with given section data and given sectioncurve data obtained from a blueprint (which data has already been fedinto the processor by the data input processing step [I]). Further, thecylindrical intermediate section is specified by "intermediate sectioninformation". The latter contains "section-related information" whichindicates what the ordinal number of the obtained cylindricalintermediate section in the desired curved surface is, and "sectionposition information", such as a transformation matrix, which indicateshow to transform a specific coordinate system to obtain the derivedcylindrical intermediate section.

The methods of generating a cylindrical intermediate section will bedescribed next.

(1) Method I of generating a cylindrical intermediate section

As mentioned earlier, in a case where one cylindrical section (givencylindrical surface) 101 is given (FIG. 3), cylindrical intermediatesections 103, 104, 105 . . . are generated concentrically with respectto the given cylindrical surface 101. Thus, if we let R1 denote theradius of the given cylindrical surface and let R3, R4, R5 . . . denotethe radii of the cylindrical intermediate sections 103, 104, 105 . . . ,respectively, then the intermedate cylindrical sections 103, 104, 105 .. . should be generated so as to achieve concentricity and satisfy therelationship R1<R3<R4<R5.

(2) Method II of generating a cylindrical intermediate section

As mentioned earlier, in a case where two cylindrical surfaces 101, 102(FIG. 4(a)) are given, the cylindrical intermediate section 103 isgenerated in such a manner that the central axis O is shiftedsuccessively from central axis O₁ to central axis O₂, that the radius Rgrows successively larger from R1 to R2, and that the central axesremain in parallel. In other words, letting O₁ O:OO₂ =m:n in FIG. 4(b),the intermediate cylindrical section 103 is generated so as to have theradius R given by the following equation:

    R=R1+m (R2-R1)/m+n                                         (1)

If m/n is successively increased from 0:1 to 1:0, then intermediatecylindrical sections will be generated one after another. It should benoted that the generated intermediate cylindrical section will coincidewith the given cylindrical surface 101 when m:n=0:1 holds, and with thegiven cylindrical surface 102 when m:n=1:0 holds.

After the intermediate cylindrical surface has been generated by MethodI or II described above, processing is executed for the generation of acylindrical intermediate section curve lying on the intermediatecylinder.

[III] Processing for cylindrical intermediate section curve generation

A cylindrical intermediate section curve is generated by any one of thefollowing methods I through IV of cylindrical intermediate section curvegeneration in accordance with the given section curve data of theparticular section on the blueprint. The following procedure is followedfor each method:

(1) obtaining the desired intermediate section-related information;

(2) transforming each given cylindrical section curve, as well as theinterval formed by two reference curves, in such fashion that they lieon the same predetermined plane (H-θ plane);

(3) generating a cylindrical intermediate section curve on the planeinto which the transformation has been made (H-θ plane); and

(4) transforming the cylindrical intermediate section curve on the H-θplane into one which lies in the desired intermediate cylindricalsection in space.

(1) Method I of generating a cylindrical intermediate section curve

Method I of cylindrical intermediate section curve generation isapplicable to a case where data relating to two cylindrical sectioncurves and one reference curve is given, as shown in FIG. 7(a).Hereafter reference will be had to FIGS. 7(b) to 7(f) to describe theprocedure for generating a cylindrical intermediate section curveaccording to Method I.

(1) Section-related information (the dividing ratio m/n) concerning thedesired intermediate cylindrical surface 103 is obtained.

(2) The given cylindrical section curves 101a, 102a on the givencylindrical surfaces 101, 102 are transformed so as to lie on the sameplane (on the H-θ plane) [FIG. 7(b)]. It should be noted that the givencylindrical section curves 101a, 102a can be considered to be curves onthe same H-θ plane by performing the following operations (2-1) through(2-3) after the curves 101a, 102a are transformed into the H-θ plane.

(2-1) The points of intersection P1, P1' of the reference curve 111a andboth given cylindrical surfaces 101, 102 are made the same point.

(2-2) The lines of intersection HL, HL' of the reference section 111 andthe given cylindrical surfaces 101, 102 are partitioned by the points ofintersection P1, P1'. Of these partitioned segments, those that have thesame direction with respect to the reference curve 111a are superposed.

(2-3) When straight lines VL, VL', which pass through the points ofintersection P1, P1' of the reference curve 111a and the givencylindrical surfaces and which at the same time are perpendicular to thelines HL, HL', are considered, it is seen that these straight lines VL,VL' are partitioned by the points of intersection P1, P1', respectively.Of these partitioned segments, those that have the same direction withrespect to the reference curve 111a are superposed. That is, when thegiven cylindrical surfaces 101, 102 are cut along the respective linesof intersection HL, HL' and then developed into a plane, thetransformation into an identical plane is achieved by superposing VL,VL' and HL, HL' and P1, P1'.

(3) By using the two given section curves 101a', 102a' lying in thepredetermined plane obtained from step (2) above, an intermediatesection curve 103a' is generated in said plane [FIG. 7(c)].

The intermediate section curve 103a is generated through the followingprocedure:

(3-1) Points Q1, Q2, which partition the lengths of the respective givensection curves 101a', 102a' each into a ratio of a:b, are found [FIG.7(d)]. The following steps (3-1-1) through (3-1-4) are observed to findthe points that partition the given section curves 101a', 102a' into theratio a:b:

(3-1-1) The length of each element constituting the given section curvesis found (where the term "element" is taken to mean a line segment or anarc constituting the given curve), and these lenghs are added togetherto find the total length D of each curve.

(3-1-2) D' is evaluated from ##EQU1##

(3-1-3) An element is extracted containing a point at a distance D' fromone end, which point serves as a reference point for partitioning. If D₁is taken as the length of the initial element, D₂ as the length of thenext element, D_(i) as the length of the i-th element and so on, theextraction of elements is carried out by finding the k that satisfiesthe following inequality: ##EQU2##

(3-1-4) This step is to find the point on the k-th element whosedistance from the starting point thereof is D", where D" is found from:##EQU3## The obtained point is that which partitions the given curveinto the ratio m:n from one end thereof. It will be assumed that, instep (3-1-3), ##EQU4## when k=1.

(3-2) A dividing point R_(i) is computed, which point partitions astraight line connecting the dividing points Q1, Q2 at the partitioningratio m:n of step (1). [See FIG. 7(e)]

If we let the coordinates of the dividing points Q1, Q2 be (x₁,y₁) and(x₂,y₂), respectively, then the coordinates R_(i) (X,Y) of the dividingpoint R_(i) may be calculated from: ##EQU5##

(3-3) The intermediate section curve 103a' is generated by a series ofpoints R_(i) (i=1,2 . . . ) obtained by successively changing the valueof the dividing ratio a/b of step (3-1) from 0 to 1 [FIG. 7(f)]. Asmoother intermediate section curve 103a' can be obtained by making thesuccessive changes in the value of a/b very small.

(4) The intermediate section curve 103a' on the θ-H plane, which sectioncurve was obtained from step (3) above, is transformed into a curvelying on the intermediate cylindrical surface 103 [FIG. 7(a)] in thedefined space.

(2) Method II of generating a cylindrical intermediate section curve

This method is applicable to a case where the available data is datarelating to one given cylindrical section curve and two referencecurves. The cylindrical intermediate section is generated in accordancewith Method I described above.

The procedure for generating a cylindrical intermediate section curve byMethod II will now be described with reference to FIGS. 8(a) to 8(d).

(1) Section-related information (radius R) concerning the desiredintermediate cylindrical surface 103 is obtained.

(2) The given cylindrical section curve 101a' on the given cylindricalsurface 101, and the points of intersection P1", P2" of the intermediatecylindrical surface 103 and the first and second reference curves 111a,112a, are transformed into a curve and points on the same plane (i.e.,on the H-θ plane) [FIG. 8(b)].

It should be noted that the transformation into the curve and points onthe same plane is performed through the same procedure consisting of thesteps (2-1) through (2-3) of Method I for cylindrical intermediatesection curve generation.

(3) The given cylindrical intermediate section curve 101a' and thepoints of intersection P1", P2" on the θ-H plane, as obtained in step(2), are used to generate a cylindrical intermediate section curve 103a'lying on said plane.

This intermediate section curve is generated through the followingprocedure:

(3-1) A computation is performed to obtain the ratio k/l of the lengthof the line segment connecting the starting point P1 and end point P2 ofthe given section curve 101a' resulting from the transformation into thepredetermined plane, to the length of the line segment connecting thepoints of intersection P1", P2" which have also been transformed intopoints in the predetermined plane. In addition, an angle θ is computed.The angle θ is the angle of rotation through which the line segment P1P2of the angle ∠P2P1P2" is rotated in the counter-clockwise direction tobring it into coincidence with the line segment P1"P2". Thecounter-clockwise direction is taken as the positive direction [FIG.8(c)].

(3-2) The dividing point S_(i) that divides the given section curve101a' into a ratio of a:b is computed according to the method of steps(3-1-1) through (3-1-4) as described in connection with Method I ofgenerating a cylindrical intermediate section [FIG. 8(c)].

(3-3) A computation is performed to find a point S_(i) " which resultswhen an external dividing point S_(i) ', for externally dividing theline segment PiS_(i) into a ratio of k:l, is rotated through the angle θ[FIG. 8(c)].

Letting (x_(i), y_(i)) represent the coordinates of the dividing pointSi that divides the given section curve 101a' into a ratio of a:b,letting (x_(o), y_(o)) represent the coordinates of the point P1, andletting (X, Y) represent the coordinates of the point Si", thecoordinates of the point S_(i) " are found from: ##EQU6##

(3-4) The cylindrical intermediate section curve 103a' is generated by aseries of points S_(i) " (i=1,2,3 . . . ) obtained by successivelychanging the value of the dividing ratio a/b of step (3-2) from 0 to 1[FIG. 8(d)]. A smoother intermediate section curve 103a' can be obtainedby making the successive changes in the value of a/b very small.

(4) The intermediate section curve 103a' on the θ-H plane, which sectioncurve was obtained from step (3) above, is transformed into a curvelying on the intermediate cylindrical surface 103 [FIG. 8(a)] in thedefined space.

(3) Method III of generating a cylindrical intermediate section curve

This method is applicable to a case where the available data is datarelating to two given cylindrical section curves and two referencecurves. The cylindrical intermediate section is generated in accordancewith Method II described above.

The procedure for generating a cylindrical intermediate section curve byMethod III will now be described with reference to FIGS. 9(a) to 9(d).Here Method III is a combination of the Methods I and II for cylindricalintermediate section curve generation.

(1) Information (the dividing ratio m/n, etc.) concerning the desiredcylindrical intermediate section is obtained.

(2) The given cylindrical intermediate section curves 101a, 102a on thegiven cylindrical surfaces 101, 102 and the points of intersection P1",P2" of the intermediate cylindrical surface 103 and first and secondreference curves 111a, 112a are transformed into curves and points onthe same plane (on the θ-H plane) [FIG. 9(b)].

This transformation into the same plane is performed through the sameprocedure, consisting of the steps (2-1) through (2-3), described abovein connection with Method I for cylindrical intermediate sectiongeneration.

(3) The given cylindrical intermediate section curves 101a', 102a' onthe predetermined plane obtained in step (2) above are used to generatea reference cylindrical intermediate section curve 103b lying on saidplane [FIG. 9(c)]. This reference cylindrical intermediate section curve103b is generated through the same procedure, consisting of steps (3-1)through (3-3), described in connection with Method I for cylindricalintermediate section curve generation.

(4) The reference cylindrical intermediate section curve 103b and thepoints of intersection P1", P2" on the predetermined plane obtained instep (3) above are used to generate a cylindrical intermediate sectioncurve 103a' on said plane. This cylindrical intermediate section curve103a' is generated through the same procedure, consisting of steps (3-1)through (3-4), described in connection with Method II for cylindricalintermediate section curve generation [FIG. 9(d)].

(5) The cylindrical intermediate section curve 103a' on the θ-H planeobtained in step (4) above is transformed into a curve on theintermediate cylindrical surface 103 in the defined space [FIG. 9(d)].

(4) Method IV of generating a cylindrical intermediate section curve

This method is applicable to a case where the available data is datarelating to two given cylindrical section curves as shown in FIG. 10(a).The cylindrical intermediate section is generated in accordance withMethod II described above.

(1) Section-related information (the dividing ratio m:n) concerning thedesired intermediate cylindrical surface 103 is found.

(2) The given cylindrical section curves 101a, 102a are developed intocurves on the same predetermined plane (on the θ-H plane) [FIG. 10(b)].

(3) The cylindrical intermediate section curve 103a' on the θ-H plane isfound after connecting the corresponding points Qi, Qi' and obtainingthe point R_(i) (i=1,2 . . . ) that internally divides the connectingline into the ratio m:n.

(4) The intermediate section curve 103a' on the θ-H plane obtained instep (3) above is transformed into a curve on the intermediatecylindrical surface 103 in the defined space [FIG. 10(a)].

[IV] Processing for curved surface generation

A number of the given section curves 103a are obtained when theforegoing processing for cylindrical intermediate section generation andprocessing for cylindrical intermediate section curve generation arerepeated while successively changing the dividing ratio m:n from 0:1 to1:0 or while successively increasing the radius R. A smooth curvedsurface can then be generated by connecting these curves. A smoothercurved surface can be obtained by making the successive changes in theratio m:n very small. FIGS. 11(a) to 11(e) show examples of surfacesgenerated by the method of the present invention, in which 11(a) through11(d) are for cases where the surfaces are generated by Methods Ithrough IV of cylindrical intermediate section curve generation,respectively, and in which (e) is for a case where one cylindricalsection curve 101a and a reference curve 111a are given.

FIG. 12 is a block diagram showing a curved surface generating apparatusfor practicing the present invention. In the Figure, numeral 301 denotesa data input unit for entering section data (reference sections,cylindrical sections) and section curve data (reference curves,cylindrical section curves) given on the blueprint, as well as forentering other data. Numeral 302 denotes a memory for storing thesection data and section curve data, as well as cylindrical intermediatesection data and cylindrical intermediate section curve data and thelike generated by a cylindrical intermediate section generating deviceand cylindrical intermediate section curve generating device which willbe described below. Numeral 303 denotes the cylindrical intermediatesection generating device which generates a cylindrical intermediatesection using the section data and section curve data stored in thememory 302, as well as information indicative of which of the Methods Iand II for cylindrical intermediate section generation is to be used togenerate a cylindrical intermediate section (intermediate cylindricalsurface), and which stores the cylindrical intermediate section data,relating to the cylindrical intermediate section, in the memory 302.Numeral 304 denotes the cylindrical intermediate section curvegenerating device which, using the section data, section curve data andcylindrical intermediate section data, as well as information indicativeof which of the Methods I through IV for cylindrical intermediatesection curve generation is to be used to generate a cylindricalintermediate section curve, generates the particular cylindricalintermediate section curve in accordance with the abovementioned steps,and which stores the cylindrical intermediate section curve data,relating to the cylindrical intermediate section curve, in the memory302. Numeral 305 denotes a tape creation control unit for reading, fromthe memory 302, such data as the stored cylindrical intermediate sectiondata and stored data relating to the cylindrical intermediate sectioncurves lying on the cylindrical intermediate sections, and fordelivering this data upon converting it into an NC tape format formachining a metal mold or the like. Numeral 306 denotes a controlcircuit for controlling the memory 302, cylindrical intermediate sectiongenerating device 303, cylindrical intermediate section curve generatingdeviced 304, and tape creation control unit 305. Numeral 307 denotes atape puncher, 308 a paper tape, and 309 a printer.

This apparatus for generating curved surfaces sequentially generatescylindrical intermediate section curves in accordance with theprocessing steps for cylindrical intermediate section generation andcylindrical intermediate section curve generation, described above, andconverts the cylindrical intermediate section curve data into a tapeformat before delivering the data to the tape puncher 307 or printer309.

Industrial Applicability

In a case where cylindrical sections and cylindrical section curveslying in these sections are given, the present invention makes itpossible to create the surface bounded by these curves. In addition, themethod of the present invention makes it possible to create, in a simplemanner, sophisticated three-dimensional bodies through processing by asmall-scale computer. With the conventional computerized methods, on theother hand, the patch system requires the processing of large quantitiesof data and complicated mathematical processing, and requires also theuse of a large-scale computer, while the system which enables the use ofa small computer does not permit a three-dimensional tool offset, limitsmovement of the cutting tool and places a restriction upon the machinedshape, thereby making it impossible to create sophisticatedthree-dimensional surfaces.

Combining the method of the present invention with the previouslyproposed method of surface creation will make it possible to createalmost any mold surface required in NC machining. The present inventiontherefore has a very high degree of industrial application.

What is claimed is:
 1. A method of generating a curved surface of athree dimensional body, comprisingproviding at least two given sectionsand respective given section curves to include at least a first givencylindrical section and a respective first given cylindrical sectioncurve, each said given cylindrical section having an axis parallel to afirst direction, generating a plurality of intermediate cylindricalsections so that the axis of each said cylindrical intermediate sectionis parallel to said first direction, and so that each said given andintermediate cylindrical section does not intersect each other, andgenerating a respective intermediate cylindrical section curve in saidintermediate section from said given section curves in said givensections, and from the respective radii, and any separation between theaxes, of the given and intermediate cylindrical sections, wherein, whensaid given sections and respective given section curves include only onegiven cylindrical section and one respective given cylindrical sectioncurve, then all of said given and intermediate cylindrical sections areconcentric and said given sections and respective given section curvesinclude two reference sections and respective reference section curves.2. The method of claim 1, comprisingproviding a second one of said givencylindrical sections that is non-concentric with said first givencylindrical section and a respective second one of said givencylindrical section curves, the respective radii of said first andsecond given cylindrical sections being R₁ and R₂, forming a firststraight line connecting the axes of said first and second givencylindrical sections, and dividing said first straight line at each of aplurality of dividing points into a respective plurality of pairs oflengths m and n, each said pair of lengths defining a respective ratiom/n, taking a respective plurality of second straight lines that areparallel to said first direction and which pass through said dividingpoints as the axes of respective ones of said intermediate cylindricalsections, and generating each respective one of said intermediatecylindrical sections in such a manner that its radius R is

    R=R.sub.1 +m(R.sub.2 -R.sub.1)/(m+n)

for the respective values of m and n.
 3. The method of claim 2,comprisingproviding said given sections and given section curves toinclude a reference section and a respective reference section curve,said reference section having respective lines of intersection with saidfirst and second given cylindrical sections, and said reference sectioncurve having respective points P₁, P₁ ' of intersection with said firstand second cylindrical section curves, developing said first and secondgiven cylindrical section curves in a first plane, computing each saidintermediate cylindrical section curve in said first plane based on therespective ratio m/n and on said first and second given cylindricalsection curves, and transforming each intermediate cylindrical sectioncurve in said first plane into the respective intermediate cylindricalsection in such a manner that each said intermediate cylindrical sectioncurve has a respective point of intersection P₁ "' with the givenreference section curve.
 4. The method of claim 3, wherein saiddeveloping of said first and second given cylindrical section curves,and said computing of each intermediate cylindrical section curve foreach said ratio m/n in said first plane, comprisestransforming each ofsaid first and second given cylindrical section curves into apredetermined plane coordinate system in said first plane in such amanner that said points of intersection P₁ and P₁ ', of the first andsecond given cylindrical section curves with the reference sectioncurve, coincide, and that said lines of intersection of each of thefirst and second given cylindrical sections with said reference sectioncoincide, computing a respective first point Q₁, Q₂, on said first andsecond cylindrical section curves, by internally dividing into a ratioof a/b each of said first and second cylindrical section curvestransformed into said predetermined plane coordinate system, and byinternally dividing into the respective ratio of m/n a third straightline connecting the respective first points Q₁, Q₂ on said first andsecond given cylindrical section curves, and computing the respectiveintermediate cylindrical section curve in said predetermined planecoordinate system for each said ratio m/n by computing a plurality ofsaid first points corresponding to a plurality of values for the ratioa/b.
 5. The method of claim 1, comprisingproviding said given sectionsand given section curves to include two reference section curves andrespective reference section curves, wherein said first givencylindrical section intersects each of said two reference sections atrespective first and second intersection lines and the first and secondof said two reference section curves intersect said first givencylindrical section curve at respective starting and end points P₁, P₂said first given cylindrical section curve, and all of said given andintermediate cylindrical section curves are concentric, developing in afirst plane respective points of intersection P₁ ", P₂ " of each saidintermediate cylindrical section with the first and second referencesection curves, computing each respective intermediate cylindricalsection curve in said first plane by using said first given cylindricalsection curve, and transforming each said intermediate cylindricalsection curve in said first plane into respective intermediatecylindrical section in such a manner that respective starting and endpoints of the respective intermediate cylindrical section curve coincidewith the respective points of intersection P₁ ", P₂ " of the respectiveintermediate cylindrical section curve with the two reference sectioncurves.
 6. The method of claim 5, said developing of said points ofintersection P₁ ", P₂ " and said computing of each said intermediatecylindrical section curve in said first plane includingtransforming saidfirst given cylindrical section curve and the respective points P₁ ", P₂" into a predetermined plane coordinate system in such a manner thatsaid point P₁ and the respective point P₁ " coincide and said first andsecond intersection lines coincides, computing a ratio 1₁ /1₂, wherein1₁ is the length of a straight line P₁ P₂ connecting said points P₁ andP₂ in said predetermined plane coordinate system and 1₂ is the length ofa straight line P₁ "P₂ " connecting said points P₁ ", P₂ " in saidpredetermined plane coordinate system, finding a point S_(i) whichinternally divides said first given cylindrical section curve in saidpredetermined plane coordinate system into a selected ratio of a/b,computing a first angle equal to the angle between said straight line P₁P₂ and said straight line P₁ "P₂, computing a point S_(i) " obtainedupon rotating by said first angle, around the point P₁ in saidpredetermined plane coordinate system, a further point S_(i) ' which isdefined by extending the line P₁ S_(i) by the factor 1₂ /1₁, andgenerating the respective intermediate cylindrical section curve in saidpredetermined plane coordinate system by finding a plurality of saidpoints S_(i) " corresponds to different values for said ratio a/b. 7.The method of claim 1, comprisingproviding said given sections andsection curves to include a second given cylindrical section and arespective second given cylindrical section curve, said first and secondgiven cylindrical sections having respective radii R₁ and R₂, and firstand second reference sections and respective first and second referencesection curves, each of said first and second given cylindrical sectioncurves intersecting said first reference section curve at respectivepoints P₁ and P₁ ', each of said first and second given cylindricalsection curves intersecting said second reference section curve atrespective points P₂ and P₂ ', and each of said first and secondreference sections intersecting at respective intersecting lines each ofsaid first and second given cylindrical sections, dividing a firststraight line connecting the axes of the first and second givencylindrical sections at each of a plurality of dividing points into arespective pair of lengths m and n defining a respective ratio m/n,forming a plurality of second straight lines passing through saiddividing points as the respective axes of said intermediate cylindricalsections, generating each said intermediate cylindrical section with arespective radius R given by

    R=R.sub.1 +m(R.sub.2 -R.sub.1)/(m+n)

for the respective values of m and n, developing said first and secondgiven cylindrical section curves with respective starting and end pointsP₁ corresponding to said points of intersection P₁, P₂ and P'₁, P'₂ withthe first and second given reference curves in a first plane, computingeach said intermediate cylindrical section curve in said first plane,corresponding to each respective ratio m/n, by using said first andsecond given cylindrical section curves, and transforming each saidintermediate cylindrical section curve in said first plane into therespective intermediate cylindrical section in such a manner thatrespective starting and end points P₁ ", P₂ " of each intermediatecylindrical section curve coincide with the respective points ofintersection of the intermediate cylindrical section with said first andsecond reference curves.
 8. The method of claim 7, said developing andcomputing in said first plane, for each respective m/n ratio,comprisingtransforming into a predetermined plane coordinate system insaid first plane each of said first and second given cylindrical sectioncurves and the respective starting and end points P₁ ", P₂ " of eachrespective intermediate cylindrical section in such a manner that saidpoints P₁, P₁ ' of intersection of said given cylindrical section curveswith first said reference section curve, and said point P₁ " ofintersection of each respective intermediate cylindrical section curvewith said first reference section curve coincide, and all of said linesof intersection of the first reference section with said first andsecond given cylindrical sections coincide, computing a point Ri byinternally dividing, at respective dividing points Q₁, Q₂, into a ratioof a/b, each of said first and second given cylindrical section curvestransformed into said predetermined plane coordinate system, and byinternally dividing a third straight line connecting the dividing pointsQ1, Q2, according to the respective m/n ratio, generating a respectivefurther curve P₁ Pe for each said intermediate cylindrical section curveby computing a plurality of said points Ri with respectively differentinternal dividing ratios a/b, said curve P₁ Pe having an end point Pecorresponding to said dividing point corresponding to said points P₂, P₂', computing a ratio 1₁ /1₂, wherein 1₁ is the length of a straight lineP₁ Pe connecting the starting point P₁ and the end point Pe of saidcurve P₁ Pe and 1₂ is the length of a straight line P₁ P₂ " connectingsaid points P₁, P₂ " transformed into the plane coordinate system,computing a first angle in said plane coordinate system between saidstraight line P₁ Pe and said straight line P₁ P₂, computing a pointS_(i) " obtained upon rotating by said first angle a further point S_(i)' which is defined by extending said straight line P₁ S_(i) by a factorof 1₂ /1₁, and generating each respective intermediate cylindricalsection curve in said predetermined plane coordinate system by finding aplurality of said points S_(i) " having corresponding different valuesfor the ratio a/b.
 9. The method of claim 1, comprisingproviding saidgiven sections and given section curves to include a second cylindricalsection curve in a respective second cylindrical section, said first andsecond given cylindrical sections being non-concentric and havingrespective radii R₁, R₂, dividing a first straight line connecting theaxes of the first and second given cylindrical sections by a pluralityof dividing points into a plurality of pairs of lengths m and n, eachsaid pair of lengths defining a respective ratio m/n, taking a pluralityof second straight lines passing through said dividing points as therespective axes of said intermediate cylindrical sections, andgenerating each said intermediate cylindrical section with a respectiveradius R given by

    R=R.sub.1 +m(R.sub.2 -R.sub.1 /(m+n)

for the respective pair of lengths m and n, developing each of saidfirst and second given cylindrical section curves in a first plane,generating an intermediate cylindrical section curve for each of saidlength ratios m/n by connecting with a third straight line correspondingpoints on each of the first and second given cylindrical section curvesin the first plane and finding the dividing point on each said thirdstraight line which divides the second straight line into the respectiveratio m/n, and transforming each generated intermediate cylindricalsection curve into the respective intermediate cylindrical section. 10.A method of generating a curved surface of a three dimensional body,comprisingproviding at least two given sections and respective givensection curves to include at least a first given cylindrical section anda respective first given cylindrical section curve, each said givencylindrical section having an axis parallel to a first direction,generating a plurality of intermediate cylindrical sections in such amanner that the axis of each said cylindrical intermediate section isparallel to said first direction, and each said given and intermediatecylindrical section does not intersect each other, and generating arespective intermediate cylindrical section curve in each saidintermediate cylindrical section from said given section curves, andfrom the radii, and any separation between the axes, of the given andintermediate cylindrical sections.
 11. The method of claim 10,comprisingproviding said given sections and given section curves toinclude two reference section curves and respective reference sections,wherein said first given cylindrical section intersects each of said tworeference sections at respective first and second intersection lines andthe first and second of said two reference section curves intersect saidfirst given cylindrical section curve at respective starting and endpoints P₁, P₂ of said first given cylindrical section curve, developingin a first plane respective points of intersection P₁ ", P₂ " of eachsaid intermediate cylindrical section with the first and secondreference section curves, computing each respective intermediatecylindrical section curve in said first plane by using said first givencylindrical section curve, and transforming each said intermediatecylindrical section curve in said first plane into respectiveintermediate cylindrical section so that respective starting and endpoints of the respective intermediate cylindrical curve coincide withthe respective points of intersection P₁ ", P₂ " of the respectiveintermediate cylindrical section curve with the two reference sectioncurves.
 12. The method of claim 11, said developing of said points ofintersection P₁ ", P₂ " and said computing of each said intermediatecylindrical section curve in said first plane includingtransforming saidfirst given cylindrical section curve and the respective points P₁ ", P₂" into a predetermined plane coordinate system in such a manner thatsaid point P₁ and the respective point P₁ ' coincide and said first andsecond intersection lines coincide, computing a ratio 1₁ /1₂, wherein 1₁is the length of a straight line P₁ P₂ connecting said points P₁ and P₂in said predetermined plane coordinate system and 1₂ is the length of astraight line P₁ "P₂ " connecting said points P₁ ", P₂ " in saidpredetermined plane coordinate system, finding a point S_(i) whichinternally divides said first given cylindrical section curve in saidpredetermined plane coordinate system into a selected ratio of a/b,computing a first angle equal to the angle between said straight line P₁P₂ and said straight line P₁ "P₂ ", computing a point S_(i) " obtainedupon rotating by said first angle, around the point P₁ in saidpredetermined plane coordinate system, a further point S_(i) ' which isdefined by extending the line P₁ S_(i) by the factor 1₂ /1₁, andgenerating the respective intermediate cylindrical section curve in saidpredetermined plane coordinate system by finding a plurality of saidpoints S_(i) " corresponding to different values for said ratio a/b. 13.The method of claim 10, comprisingproviding said given sections andsection curves to include two cylindrical sections of radii R₁ and R₂,wherein R₂ >R₁, and two respective cylindrical sections, and providingeach said intermediate cylindrical section to have a radius R given by arespective ratio m/n according to

    m/n=(R-R.sub.1)/(R.sub.2 -R)

wherein the ratio m/n is the ratio of the separation between the givencylindrical section of radius R₁ and the respective intermediatecylindrical section to the spacing between the respective intermediatecylindrical section and the given cylindrical section of radius R₂.